Statistical Analysis for Physics Research Project

Important concepts for Problem: Chi-Square test, p-value, Sigma Significance

I am an undergraduate Physics student working on a research project which involves a certain level of statistical analysis that I have some lacking knowledge about. I have built a macro that has the capability to output both Chi^2 and p-value test scores between two histograms, one filled by a simulation of neutrino event counts and the other filled by this same simulation while incorporating a theory of heavy neutrinos. My professor has now tasked me with converting my sensitivity scores into a form that I do not have an equation or method to obtain.

Goal: To convert the p-value or chi^2 score into a sensitivity score in terms of a constant multiplied by the standard deviation of a normal distribution called the “Sigma Significance”. An example of a score like this would be 1.57*(sigma) or 0.82*(sigma) in which a high amount would correspond to a lower p-value and higher Chi^2 while a low sigma significance would correspond to a high p-value and low Chi^2 score.

Tldr; I want to convert a chi-square or p-value to the significance in terms of the standard deviation.

If any other information may be needed to solve this problem please let me know and I can try and provide it.

Dear @DTMsurf,

Could you please attach the macro? Other than that, I cannot help you, but maybe @moneta knows.



The function you are probably looking for is RooStats::PValueToSignificance converting a p value in a significance measured as sigma of a normal distribution.
It returns the one-side significance, if you are doing a two-side test, then you will have to divide the p-value by 2 before passing to the function.


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